Pith Number

pith:7X63YGMR

pith:2022:7X63YGMRXSFCBCGCEASL4DYFK4

not attested not anchored not stored refs pending

Branching Random Walks on relatively hyperbolic groups

Longmin Wang, Matthieu Dussaule, Wenyuan Yang

arxiv:2211.07213 v1 · 2022-11-14 · math.PR · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7X63YGMRXSFCBCGCEASL4DYFK4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Dimension jump at the uniqueness threshold for percolation in $\infty+d$ dimensions

Receipt and verification

First computed	2026-07-05T05:15:51.036267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdfdbc1991bc8a2088c22024be0f05570034bdc5cb0772c0f3397a4effcf46f9

Aliases

arxiv: 2211.07213 · arxiv_version: 2211.07213v1 · doi: 10.48550/arxiv.2211.07213 · pith_short_12: 7X63YGMRXSFC · pith_short_16: 7X63YGMRXSFCBCGC · pith_short_8: 7X63YGMR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7X63YGMRXSFCBCGCEASL4DYFK4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fdfdbc1991bc8a2088c22024be0f05570034bdc5cb0772c0f3397a4effcf46f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e48736ecdd36ebf58485ba4457556db6144d8e5b8dccbcf7fed907e809dd658a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-11-14T09:03:34Z",
    "title_canon_sha256": "442bc12db40aeae9301cf4e05f9bd04377ea6d4c66fc06d8d1d08443f4b8e417"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.07213",
    "kind": "arxiv",
    "version": 1
  }
}